Cryptology ePrint Archive: Report 2009/409

A Tree Based Recursive Scheme for Space Efficient Secret Sharing

Abhishek Parakh and Subhash Kak

Abstract: This paper presents a k-out-of-n recursive secret sharing scheme based on an n-ary tree data structure. In recursive hiding of secrets, the user encodes additional secrets in the shares of the secret intended to be original shared without an expansion in the size of the latter, thereby decreasing the effective share size per secret and increasing the overall space efficiency of secret sharing, with a trade-off in security. The proposed scheme has applications in secure distributed storage and information dispersal protocols. It may be used as a steganographic channel to transmit hidden information in secret sharing, which may be used for authentication and verification of shares and the reconstructed secret itself.